5 you are given the following information the current

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5. You are given the following information. The current dollar - pound exchange rate is $2 per British pound. A U.S. basket that costs $100 would cost $120 in the United Kingdom. For the next year, the Fed is predicted to keep U.S. inflation at 2% and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergence to absolute PPP is 15% per year. a. What is the expected U.S. minus U.K. inflation differential for the coming year? Answer: The inflation differential is equal to 1% ( 2% 3%). b. What is the current U.S. real exchange rate, q UK / US , with the United Kingdom? Answer: The current real exchange rate is: q UK / US ( E $/£ P UK )/ P US $120/$100 1.2. c. How much is the dollar overvalued/undervalued? Answer: The British pound is undervalued by 20% and the U.S. dollar is over- valued by 20% ( 1.2 1 / 1). d. What do you predict the U.S. real exchange rate with the United Kingdom will be in one year’s time? Answer: We can use the information on convergence to compute the implied change in the U.S. real exchange rate. We know the speed of convergence to ab- solute PPP is 15%; that is, each year the exchange rate will adjust by 15% of what is needed to achieve the real exchange rate equal to 1 (assuming prices in each country remain unchanged). Today, the real exchange rate is equal to 1.2, imply- ing a 0.2 decrease is needed to satisfy absolute PPP. Over the next year, 15% of this adjustment will occur, so the real exchange rate will decrease by 0.03. There- fore, after one year, the U.S. real exchange rate, q UK/US , will equal 1.17. e. What is the expected rate of real depreciation for the United States (versus the United Kingdom)? Answer: From (d), the real exchange rate will decrease by 0.03. Therefore, the rate of real depreciation is equal to 2.5% ( 0.03 1.20). This implies a real appreciation in the United States relative to the United Kingdom. f. What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)? Answer: The expected rate of nominal depreciation can be calculated based on the inflation differential plus the expected real depreciation from (e). In this case, the inflation differential is 1% and the expected real appreciation is 2.5%, so the expected nominal depreciation is 3.5%. That is, we expect a 3.5% appreciation in the U.S. dollar relative to the British pound. g. What do you predict will be the dollar price of one pound a year from now? Answer: The current nominal exchange rate is $2 per pound and we expect a 3.5% appreciation in the dollar (from [f]). Therefore, the expected exchange rate in one year is equal to $1.93 ( $2 (1 0.035). 6. Describe how each of the following factors might explain why PPP is a better guide for exchange rate movements in the long run versus the short run: (1) transactions costs, (2) nontraded goods, (3) imperfect competition, and (4) price stickiness. As mar- kets become increasingly integrated, do you suspect PPP will become a more useful guide in the future? Why or why not?
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